The first number in the sequence is 3 because there are three letters in the word "one",
the second number in the sequence is 3 because there are three letters in the word "two",
the third number in the sequence is 5 because there are five letters in the word "three",
etc.

That's what they're asking for: the number of letters in the english word for each number in sequence.

Re: nth term - English word for index n

That's just what "the number of letters in the English word for the index n" means! then 10th number in the sequence is 3 because the word "ten" has 3 letters. What is the eleventh number? (Be careful, it is not 8!)